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Published online by Cambridge University Press: 20 January 2009
Laguerre has shown that if 
be expanded in ascending powers of t,
where fn(x) is a polynomial of degree n, satisfying the differential equation
* Laguerre, , Œuvres, T. I., p. 436Google Scholar. Abel, , Œuvres, T. II., p. 284. (1881).Google Scholar
* The result requires modification if p is a negative integer. In this case the second solution of (6) is required to express the coefficients for which n > −p.
* Loc. Cit., p. 428.
* Theorie des Integrallogarithmus, Leipzig (1906); p. 45
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